3.0 The Principle of Least Action We consider two
paths, one with velocity c in one medium, the other with
velocity v in another. In order to go from one point two
another over two paths, the refraction is such that the sine
of the angle of incidence equals the sine of the angle of
refraction.
We have the two paths are travelled in a time t:
This is the mysterious Nature of reality, the path of least
time is taken. This falls under the general heading The
Principle of Least Action, attributed to firstly the French
Natural Philosopher and mathematician Louis Maupertuis
of the early eighteenth century. I say mysterious, because
as it is said in physics, for something to know the path of
least action and take it, it is as if it has explored first all
paths between A and B to know which one would be the
path of least action. Everything in physics comes to this
principle. It is called a principle, not a theory, law, or rule.
Yet it seems to be the way Nature behaves, and it is
mysterious. Richard Feynman applied it to quantum
mechanics, probably because the mysterious Planck’s
constant that governs quantum mechanics is in Joule-
seconds, energy over time, and this is the terms in which
action is formulated mathematically.
In our scenario here we regard matter, the proton in
particular, as the cross-section of a hypersphere. Our two
mediums are hyperspace and space and the least action
principle applies in the same mathematical form. This is
abstract cosmology, that really is the underlying
mathematics is common to all systems, that in effect they
are manifestations of one another.
We have